Answer:
1. Their ages are:
Steve's age = 18
Anne's age = 8
2. Their ages are:
Max's age = 17
Bert's age = 11
3. Their ages are:
Sury's age = 19
Billy's age = 9
4. Their ages are:
The man's age = 30
His son's age = 10
Step-by-step explanation:
1. We make the assumption that:
S = Steve's age
A = Anne's age
In four years, we are going to have:
S + 4 = (A + 4)2 - 2 = 2A + 8 - 2
S + 4 = 2A + 6 .................. (1)
Three years ago, we had:
S - 3 = (A - 3)3
S - 3 = 3A - 9
S = 3A - 9 + 3
S = 3A – 6 …………. (2)
Substitute S from (2) into (1) and solve for A, we have:
3A – 6 + 4 = 2A + 6
3A – 2A = 6 + 6 – 4
A = 8
Substitute A = 8 into (3), we have:
S = (3 * 8) – 6 = 24 – 6
S = 18
Therefore, we have:
Steve's age = 18
Anne's age = 8.
2. We make the assumption that:
M = Max's age
B = Bert's age
Five years ago, we had:
M - 5 = (B - 5)2
M - 5 = 2B - 10 .......................... (3)
A year from now, it will be:
(M + 1) + (B + 1) = 30
M + 1 + B + 1 = 30
M + B + 2 = 30
M = 30 – 2 – B
M = 28 – B …………………… (4)
Substitute M from (4) into (3) and solve for B, we have:
28 – B – 5 = 2B – 10
28 – 5 + 10 = 2B + B
33 = 3B
B = 33 / 3
B = 11
If we substitute B = 11 into equation (4), we will have:
M = 28 – 11
M = 17
Therefore, their ages are:
Max's age = 17
Bert's age = 11.
3. We make the assumption that:
S = Sury's age
B = Billy's age
Now, we have:
S = B + 10 ................................ (5)
Next year, it will be:
S + 1 = (B + 1)2
S + 1 = 2B + 2 .......................... (6)
Substituting S from equation (5) into equation (6) and solve for B, we will have:
B + 10 + 1 = 2B + 2
10 + 1 – 2 = 2B – B
B = 9
Substituting B = 9 into equation (5), we have:
S = 9 + 10
S = 19
Therefore, their ages are:
Sury's age = 19
Billy's age = 9.
4. We make the assumption that:
M = The man's age
S = His son's age
Therefore, now, we have:
M = 3S ................................... (7)
Five years ago, we had:
M - 5 = (S - 5)5
M - 5 = 5S - 25 ................ (8)
Substituting M = 3S from (7) into (8) and solve for S, we have:
3S - 5 = 5S – 25
3S – 5S = - 25 + 5
-2S = - 20
S = -20 / -2
S = 10
Substituting S = 10 into equation (7), we have:
M = 3 * 10 = 30
Therefore, their ages are:
The man's age = 30
His son's age = 10
where b₁ and b₂ are the bases of the trapezoid and h is the height of the trapezoid.